Qm Definition and 1000 Threads

The hybrid QM/MM (quantum mechanics/molecular mechanics) approach is a molecular simulation method that combines the strengths of ab initio QM calculations (accuracy) and MM (speed) approaches, thus allowing for the study of chemical processes in solution and in proteins. The QM/MM approach was introduced in the 1976 paper of Warshel and Levitt. They, along with Martin Karplus, won the 2013 Nobel Prize in Chemistry for "the development of multiscale models for complex chemical systems".

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  1. J

    Coefficients of a particle in Linear superposition (QM)

    Homework Statement a particle is in a linear superposition of two states with energy E_0 \ and\ E_1 |\phi> = A|E_0> + \frac{A}{(3-\epsilon)^{1/2}}|E_1> where: A \ > \ 0, \ 0\ <\ \epsilon \ <\ 3 What is the value of A expressed as a function of epsilon Homework Equations P(E_0) \ +\...
  2. Elemental

    Spin Operators: Axial for QM, Polar in Clifford Algebra?

    Hello folks! New to this forum, so hoping I'm not retreading old ground. The Pauli matrices are spin angular momentum operators in quantum mechanics and thus are axial vectors. But in Clifford algebra in three dimensions they are odd basis elements and thus polar vectors. Hestenes, Baylis, other...
  3. MTd2

    Removing Static Black Hole Singularity without QM (paper)

    I thought of posting this on astrophysics or general relativity forums since it seems completely classical, but given the extraordinary claim, I am posting here. Note that one of the guys is a notable string theorist. http://arxiv.org/abs/1510.03396v1 Journey Beyond the Schwarzschild Black...
  4. F

    Does relativistic QM obey rotational symmetry?

    SO(3) is subgroup of Poicare group.Does Relativistic Quantum Mechanics obey rotational symmetry.If it is,why we do not still keep the non-relativistic concept of angular momentum(orbit angular momentum plus spin) for relativistic concept of angular momentum,but we instead replace the concept by...
  5. F

    QM probability and normal distribution

    Is there a relationship between QM probability and normal distribution ? I'm thinking about drawing probability densities as functions of phase. Thanks
  6. M

    Is Every Linear Function a Linear Combination of Basis Functions?

    Homework Statement Hi, am having difficulty with the Linear algebra in QM. We have been given a problem set and one of the questions am struggling with is as follows: Consider the space of all linear functions ##f(x) = ax + b## (x real) defined over the range ## -1 < x < 1 ##, with the scalar...
  7. stevendaryl

    Second Quantization vs Many-Particle QM

    Apparently, there are two different routes to get to quantum field theory from single-particle quantum mechanics: (I'm going to use nonrelativistic quantum mechanics for this discussion. I think the same issues apply in relativistic quantum mechanics.) Route 1: Many-particle quantum mechanics...
  8. Summer95

    What does "minimum range of uncertainty" mean in QM?

    Homework Statement [/B] The problem on where the photon will hit a screen, after passing through a single horizontal slit. I know the wavelength, slit width, magnitude of momentum of incoming photon (calculated), and distance between screen and slit. Homework Equations I just don't...
  9. Buzz Bloom

    Relationships between QM and QFT Particles

    What are the mathematical relationships (if any) between the particles as described by Quantum Mechanics and the particles described by Quantum Field Theory? A specific question related to the general question above arose in post #14 of the thread: How can a particle be a combination of other...
  10. Z

    QM explanation of electron conduction in crystal

    Suppose that a static electric field E is applied on a conductive crystal. Then, how quantum mechanics describes the electron movements in the crystal? I have been trying to find an explanation, but have not found any. As I understand it, we could treat the E field as a time-dependent...
  11. F

    About energy conservation in QM?

    Does energy conservation law still hold if the system contact with varying source of energy? Because in QM the Hamintonian of the system always commune with itself,so the conservation law still correct.But if it is,where is the exchange energy between the system and the enviroment?
  12. Safinaz

    How Can Spherical Harmonics Represent Functions with Higher Angular Dependence?

    1. Homework Statement Homework Equations Here we have to express ##\psi(\theta,\phi)## in terms of spherical harmonics ##Y_{lm}## to find the angular momentum. If ##\psi(\theta,\phi) = i \sqrt{\frac{3}{4\pi}} \sin{\theta} \sin{\phi} ##, it can be written as: $$ \frac{i}{\sqrt{2}} (Y_{1,1}-...
  13. Safinaz

    Question in variational method (QM)

    Homework Statement Hi, in this book " [Nouredine_Zettili]_Quantum_Mechanics_Concepts ", Eq. (9.133) Homework Equations I don't know how the second line had come from the first line:The Attempt at a SolutionI got only two terms such that: $$ < \psi_0| H | \psi_0 > = A^2...
  14. C

    Mathematics most used in GR and QM

    Hi all! Been a while since I was on PF and I greatly regret it. Forgot how great the community was. Anyways on to my point. I'm going into my second ywar of post secondary and planning to major in physics, and have the eventual goal of understanding both General relativity, and Quantum...
  15. gonadas91

    QM & Relativity: The Hardest Problems to Solve

    Hi everyone, according to some texts I ve read, there is not a clear definition for a quantum mechanical theory involving relativity. The most similar approach is that of Klein Gordon and Dirac equations, but there is not an analogy Schrodinger equation when we use relativity in QM. Can anyone...
  16. G

    Literature for QM to QFT step-by-step

    Hi all, can anybody help me to find literature that takes the reader on a step-by-step path from non-relativistic quantum theory to relativistic quantum theory? I imagine something like that: it starts with a single harmonic oscillator, analyzes the non-harmonic oscillator (does the...
  17. L

    QM notes with entanglement, Bell, decoherence, etc.

    Does anyone know of QM notes (or a review article) that covers entanglement, the measurement problem, Bell inequalities, decoherence, or the delayed choice experiment (or the more recent mesoscopic experiments). So to speak the more modern and the exciting aspects of QM. I think closest to that...
  18. Christian Grey

    What actually happens when light meets a surface(QED or QM)?

    I want to know what actually happens when light meets a surface like water or wood. Quantum mechanics says that objects are neither "transparent" nor "opaque". Rather a system as a whole can accept "energy packets" in certain ranges of energy and has no states available to accept other ranges...
  19. A

    Should I Take Quantum Mechanics for Electrical Engineering Research?

    Hi there PFers I'm looking into a variety of areas of research in electrical engineering at US universities. For instance, looking at the University of Texas page, there's a research specialty in EE called "plasma/quantum devices and optics." Now, this looks very interesting to me. I was...
  20. Jimster41

    QM and Crook's Fluctuation Theorem

    Is there a bridge from QM to Crook's Fluctuation Theorem and/or the Jarzynski Equality? More ambiguously, but maybe more directly, Is there thought to be a relationship between the QM-entanglement/decoherence/interference, and the SLOT? I am worried I may be missing a discussion of this, due...
  21. Pete Hammand

    QM & Consciousness: Has Theory Been Disproven?

    Just curious, but has this theory been completely disproven? Is it possible to even debate that this is the case? It seems to me that some of the founders of QM such as Heisenberg, Pauli, and even Max Planck toyed with this idea and considered it a possibility. Why is it not any more? I don't...
  22. J

    QM: Calculate Transmission Coefficient

    Homework Statement V(x) = -V ( if x > 0 ) 0 ( if x <= 0) ( V is positive constant) the transmission coefficient is not simply F2 / A2 ( with A the incident amplitude and F the transmitted amplitude ), because the transmitted wave travels at a different speed. Calculate...
  23. ZAN Nabil

    Solid State Good resources for introductory solid state physics and QM

    Hello,I'm new here and this is my first post. I am a freshman electronics and communication engineering student.I didn't study any quantum mechanics or solid state physics before(not in high school). But for my first year course i need to study solid state physics.The books we are suggested to...
  24. LarryS

    Does classical vacuum permittivity have a QM analog?

    According to Maxwell's Equations, the classical vacuum permittivity and permeability have a very important role: They determine the speed of light. But it seems like these two important concepts are not as precisely defined in the quantum world. Are there rigorous analogs of these two...
  25. A

    Are Additional Postulates Hidden in the Quantum Derivation from Galilei Algebra?

    I have a problem with the derivation of the the form of QM starting from the Lie algebra of the Galilei Group like the one given in Ballentine's cap 3. My Issue is that the procedure is shown almost as unavoidable, And my feeling is that there have to be more postulates that I'm not seeing...
  26. L

    What is the physical definition of a state in quantum mechanics?

    Mathematically, a state in QM is a ray on the Hilbert space. But: 1) How would you define "state" from a physical point of view? I know a lot of examples but not a general definition. 2) Given a specific quantum system, to find all the states and so the Hilbert space, all I have to do is to...
  27. Helios

    Collapsars vrs. QM degeneracy pressure

    The QM degeneracy pressure puts up a fight but the immensity of the star wins out. Why is this? Is the Pauli Exclusion Principle really a principle? Why does it surrender in this case?
  28. hilbert2

    Quantum Many-Particle QM Course Prep: Best Textbooks

    Hi, I'm going to have a long graduate-level course on many-body quantum mechanics next fall and I'm already trying to prepare for it. I have the lecture notes that were used in the same course two years ago, but they are hand-written and a bit tedious to read. Can anyone suggest a good textbook...
  29. B

    QM: Two coupled spins in a magnetic field

    Homework Statement Consider two spins, L and R, in a magnetic field along the z-axis, i.e. B = (0, 0, B) . The magnetic moments of the two spins are coupled to each other so that the total Hamiltonian reads H = g\mu_B\mathbf{B}\cdot(\mathbf{S}_L + \mathbf{S}_R) + J \mathbf{S}_L\cdot...
  30. B

    QM: Expectation value of raising and lowering operator

    Homework Statement Using J^2 \mid j,m_z \rangle = h^2 j(j+1) \mid j,m_z \rangle J_z \mid j,m_z \rangle = hm_z \mid j,m_z \rangle Derive that : \langle j,m_z \mid J_-J_+ \mid j,m_z \rangle = h^2[ j(j+1) - m_z(m_z+1)] Homework Equations J_- = J_x - iJ_y J_+ = J_x + iJ_y The...
  31. olgerm

    Analogues between QM- and CM N-body problem

    In CM general formulation of N-body problem is: x(N;D;T) = \iint \sum_{n=0}^{N_{max}} (\frac {(x(N;D;t)-x(n;D;t))*(m_N*m_n*G+q_N*q_n/(4*π*ε_0))}{(\sum_{d=0}^{D_{max}}((x(N;d;t)-x(n;d;t))^2))^{3/2}*m_N}) \, dt^2 Where x(N;D;T) is D´th coordinate of N´th body at time T. But to get equation of...
  32. B

    QM Sankar 2nd edition -- gram schmidt process on example 1.3.2

    Hi I was trying the gram schmidt process on example 1.3.2 page 43 as shown below u1=(3,0,0), u2=(0,1,2), u3=(0,2,5)v1=u1=(3,0,0) v2=u2-proj_(w1) u2=(0,1,2)-((<0,1,2><3,0,0>)/9)(3,0,0) However the top line inner product gives 0...
  33. Alexandre

    Funny thing I've found in David Griffiths QM textbook

    I really like the book, its the first physics textbook that I liked actually. But I've found a minor error. On page 8 (chapter 1 The Wave Function) it says that if you sum deviations from average of a random variable you'd get zero because " Δj is as often negative as positive", here's the...
  34. B

    How do we solve for equation 1.8.7 on page 33 of Shankar's QM 2nd Edition?

    Hi Folks, How do we arrive at equation 1.8.7 page 33. We have ##<i|\Omega-\omega I|V>=0##, given ##I=\Sigma_{j=1}|i><i|## we can write ##<i|\Omega-\omega \Sigma_{j=1}|i><i||V>=0## not sure how to proceed from here...
  35. Jimster41

    Does expansion a(t) affect QM probability density?

    I'm picturing a comoving particle, meaning at rest with respect to CMB? Does expansion affect the probability density, density current? I can't see how it wouldn't? But then it seems like there would have to be a uniform negative probability density current everywhere.
  36. T

    At what point should a grad student "understand" QM?

    Let me define the question better. For my purposes I'm saying a person "understand quantum mechanics" when they have what it takes to write a basic graduate level QM textbook. Maybe I'm setting the bar too high, but I'm a first-year physics grad student who can get good grades in QM classes...
  37. O

    Relativistic Boltzmann (including QM) equation from entropy?

    I'm interested in the derivation of relativistic Boltzmann equation from entropy after reading Scott Dodelson's wonderful cosmology book. Does anyone know of any good readings for this? The usual way of doing things in classical mechanics is to assume \frac{dN}{dt}= 0 and go from there; but...
  38. J

    Quantum Good books on QM with rigorous math

    I want to learn QM but in a way that i can learn both the deep mathematics, the physical intuition behind QM and the intuition behind the maths behind the QM(not many books have this). Note that this is my first attempt to learn QM and i will be watching some video lectures online,so i won't be...
  39. J

    Quantum Is Landau's book on QM suitable for undergraduates?

    Hello,i am just starting to learn Quantum Mechanics in the university at an underdrad level. I know there are a lot of great introductory books out there but i just saw that Landau's book on non-relativistic quantum mechanics has great reviews but upon seeing it,i was overwhelmed by the...
  40. A

    Position measurement in Non-Relativistic QM

    I've read several times in textbooks that in NR-QM you can measure with exact precision the position of a particle if you don't care at all for the momentum (because the uncertainty of the momentum will be infinite), it always seemed reasonable enough for me but now that I think about it, it...
  41. E

    How Can You Access Time Reversibility in Quantum Mechanics?

    In QM, time is reversible.. is there a setup where you can couple the system or interface it to classical apparatus such that you can access the time reversibility in qm and control it to reach the past and future (at least of the quantum system).. what would be this setup?
  42. G

    Radiation of accelerated charge in QM

    Hi, One of the main problems of the Rutherford model is the fact that the electrons are accelerated and hence should lose energy due to radiation. Bohr's model doesn't resolve this, it only postulates that the energy levels are quantized and energy can only be emitted or absorbed by jumping...
  43. T

    What are some good pedagogical QM papers?

    I did a search but couldn't find what I was looking for. I'm a physics student studying QM at the graduate level. I'm aware that "nobody truly understands QM" but I'd like to get as much insight and intuition as possible. Textbooks are good for learning to solve problems and learning the...
  44. stevendaryl

    Von Neumann QM Rules Equivalent to Bohm?

    Bohm's deterministic theory was designed to be equivalent to standard QM, but what I'm not sure about is whether that includes Von Neumann's rules. Von Neumann's rules for the evolution of the wave function are roughly described by: Between measurements, the wave function evolves according to...
  45. S

    Interpretation of the Heisenberg picture in QM

    I was always a bit puzzled by the Heisenberg picture (not mathematically, I'm fine with that, but conceptually) - if a "state" describes a system, how can it not be time-dependent, if the system changes? I just found an alternative way of looking at it which seems to make sense to me, but I'm...
  46. L

    Mathematically in-depth textbook for QM course

    I'm trying to decide between Dirac, Shankar, Mandl, Griffiths, Gasiorowicz, and Sakurai for an undergrad QM course. It is the first "proper" quantum course after a basic introduction in the modern physics class, but apparently it is particularly mathematically challenging, so I'm looking for a...
  47. Rajkovic

    Quantum Reality: Evidence for Everything Happening Simultaneously

    Does something in QM suggests that "everything is happening, here/now at once? Is there any evidence to prove it? (quantum reality) I saw a video about it on the internet, I will not post the source, because I think it is pseudoscience, but he confirmed that QM proves it..lol Please, I don't...
  48. K

    What Am I Missing in My Third Year QM Assignment Solution?

    See the picture below for details. I have included my solution thus far, but it doesn't feel right and I'm just wondering what I am missing. Any assistance would be greatly appreciated, cheers.
  49. Noctisdark

    Reflected and Transmitted wavefunction (QM)

    Homework Statement I'm asked to calculate the reflected and transmitted part of the wavefunction, in fact, this is the first time i encounter this so i need your assistance. Homework Equations Time independant schrodinger equation + continuity condition The Attempt at a Solution See the...
  50. A

    Pitfalls of E&M or QM without classical mechanics

    I'm an EE major doing a minor in physics. I have to take a standard intermediate electromagnetism course from the engineering department (which is just a more applied version of the physics department course). To get my minor, I was thinking about getting permission to use this course as a...
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